On Lie gradings II Original Research Article

To obtain fine gradings of gl(n,C), it is necessary to study maximal Abelian subgroups (MAD-subgroups) of diagonizable automorphisms in imageut(gl(n,C)). We described two finite sets imagen and imagen such that each MAD-subgroup consisting only from inner automorphisms is conjugated to some element of imagen and each MAD-subgroup containing at least one outer automorphism is conjugated to some element of imagen. Using these results concerning imagen we then easily find all MAD-subgroups in imageut(o(n,C)) for n not a subset of 8 and in imageut(sp(2n,C)).